Flowgraphs for the Representation of Nonlinear Systems

The development of a nonlinear flowgraph notation for the representation of a large class of nonlinear systems is the central topic of this paper. By the definition of power operator branches, exponential operator branches, switching operator branches, and limiting operator branches, it becomes possible to represent a variety of nonlinear systems. In particular, it becomes possible to represent in a very simple manner a number of different types of hysteretic systems. A study of the rules for manipulation of nonlinear flow-graphs is made, so as to bring out the procedures that might be used in reducing the complexity of such a system as that represented by the flowgraphs. Generalized flowgraph inversion procedures are developed as a consequence of the defined nonlinear branch transmittances. A variety of nonlinear systems are illustrated to indicate the broad applicability of the notation in representing such systems.